Wireless signal detection using a transformed lattice boundary

ABSTRACT

In at least some embodiments, a wireless communication system includes a transmitter that transmits a signal over a communication channel. The system also includes a receiver that receives the signal as an output of the communication channel. The receiver establishes a boundary for a transformed lattice and eliminates candidates outside the established boundary.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a non-provisional application claiming priority toU.S. Pat. App. Ser. No. 60/887,271, entitled “Hypercube Bounding OverLattice Searching Background”, filed on Jan. 30, 2007. Theabove-referenced application is incorporated herein by reference.

FIELD OF THE INVENTION

The present disclosure is directed to communication systems, and moreparticularly, but not by way of limitation, to lattice-reduction-aided(LR-aided) communication systems.

BACKGROUND

When using linear transformation in communication systems a typicaloperation is an equalization step. For example, the zero forcingequalizer takes the channel matrix H and inverts it in order to performdetection. Other equalizers include the minimum mean square errorequalizer and successive interference cancellation. All of theseequalizers can be combined with other processing such aslattice-reduction in order to perform detection. Methods and systemsthat reduce detection complexity are desirable.

SUMMARY

In at least some embodiments, a wireless communication system comprisesa transmitter that transmits a signal over a communication channel. Thesystem also comprises a receiver that receives the signal as an outputof the communication channel. The receiver establishes a boundary for atransformed lattice and eliminates candidates outside the establishedboundary.

In at least some embodiments, an electronic device comprises a processorand a receiver coupled to the processor. The receiver checks whetherreceived candidate points are within a transformed lattice boundary.

In at least some embodiments, a method for wireless signal detectioncomprises identifying a boundary for a transformed lattice. The methodfurther comprises eliminating candidates outside the boundary.

BRIEF DESCRIPTION OF THE DRAWINGS

For a detailed description of various embodiments of the invention,reference will now be made to the accompanying drawings in which:

FIG. 1 illustrates an integer lattice-based list in accordance withembodiments of the disclosure;

FIG. 2 illustrates a linear transformation on a lattice in accordancewith embodiments of the disclosure;

FIG. 3 illustrates a bounding operation for the lattice of FIG. 2 inaccordance with embodiments of the disclosure;

FIG. 4 illustrates an Minimum Mean-Squared Error (MMSE)Lattice-Reduction-Aided (LR-aided) Multiple-Input Multiple-Output (MIMO)detector in accordance with embodiments of the disclosure;

FIG. 5 shows a block diagram of a receiver in accordance withembodiments of the disclosure;

FIG. 6 illustrates a wireless communication system in accordance withembodiments of the disclosure;

FIG. 7 illustrates an electronic device in accordance with embodimentsof the disclosure; and

FIG. 8 illustrates a wireless signal detection method in accordance withembodiments of the disclosure.

NOTATION AND NOMENCLATURE

Certain terms are used throughout the following description and claimsto refer to particular system components. As one skilled in the art willappreciate, companies may refer to a component by different names. Thisdocument does not intend to distinguish between components that differin name but not function. In the following discussion and in the claims,the terms “including” and “comprising” are used in an open-endedfashion, and thus should be interpreted to mean “including, but notlimited to . . . ”. Also, the term “couple” or “couples” is intended tomean either an indirect, direct, optical or wireless electricalconnection. Thus, if a first device couples to a second device, thatconnection may be through a direct electrical connection, through anindirect electrical connection via other devices and connections,through an optical electrical connection, or through a wirelesselectrical connection.

DETAILED DESCRIPTION

It should be understood at the outset that although an exemplaryimplementation of one embodiment of the present disclosure isillustrated below, the present system may be implemented using anynumber of techniques, whether currently known or in existence. Thepresent disclosure should in no way be limited to the exemplaryimplementations, drawings, and techniques illustrated below, includingthe exemplary design and implementation illustrated and describedherein, but may be modified within the scope of the appended claimsalong with their full scope of equivalents.

Embodiments of the disclosure define a boundary for a translatedlattice. In at least some embodiments, the boundary is formed bytracking corner or edge elements of a lattice before and aftertranslation (before the translation, the lattice elements represent thetransmitted constellation). The boundary is used to identify whethertranslated lattice elements (sometimes called “entries”, “points”, or“candidates”) are within a valid search space. Translated latticeentries outside the boundary are eliminated as possible candidates.Defining a boundary and identifying whether translated lattice entriesare within a valid search space can reduce complexity of wireless signaldetection.

FIG. 1 illustrates an integer lattice-based list in accordance withembodiments of the disclosure. In FIG. 1, a definition of an integerlattice is provided as well as a description of how a lineartransformation affects a geometric shape. An integer lattice in the realvector space R^(n) is a discrete subgroup of the space R^(n) spanningthe real vector space R^(n). Integer lattices in R^(n) can be generatedfrom a basis for the space by creating all linear combinations of thebasis with integer coefficients, where the lattice elements areregularly spaced. In FIG. 1, V 102 represents V=[v₁ v₂] and is the basisused to generate an integer lattice E 104 having elements 108. Theinteger lattice E 104 represents E={m v ₁+n v ₂|m=±1, ±2, . . . ±c;n=±1, ±2, . . . , ±c} and is the linear combination of basis vectors v₁and v₂ for integer coefficients −2, −1, 0, 1, and 2. The list L 106represents L⊂E, c=2 and is a subset of the integer lattice E 104, wherec=2. In at least some embodiments, determining a list such as L involvesdefining a boundary for a translated integer lattice and identifyingwhether translated integer lattice entries are within a valid searchspace. Although the embodiments described herein involve an integerlattice, alternative embodiments may involve a floating point lattice,which requires higher complexity to process.

FIG. 2 illustrates a linear transformation on a lattice in accordancewith embodiments of the disclosure. The transformation shown in FIG. 2is illustrated in two dimensions, but the same concept extends to higherdimensions as well. In FIG. 2, a square lattice 202 is passed though amatrix H 204 (i.e., by multiplication). The matrix multiplication isnothing more than a linear transformation and is, geometrically, just astretching and squeezing of one shape into another.

As shown, the stretching and squeezing of the square lattice 202 resultsin a parallelogram lattice 206. Similarly, in two dimensions a lineartransformation on a circle produces an ellipse. The same concept extendsto higher dimensions. For example, in three dimensions a sphere becomesan ellipsoid. In dimensions four and above, a hypersphere becomes ahyperellipsoid. Also, in dimensions four and above, ahyperparallelopiped becomes another hyperparallelopiped even though thetwo objects are transformations of one another.

In a communication system, various lattice shapes such as thosedescribed herein may represent transmitted data. In at least someembodiments, the geometry of a translated lattice is used to placebounds on the search space. In this manner, search operations are onlyperformed within a bounded and finite geometry formed via a translationof the input finite lattice.

FIG. 3 illustrates a bounding operation for the lattice 202 of FIG. 2 inaccordance with embodiments of the disclosure. In FIG. 2, the lattice202 is an example of a standard square quadrature-amplitude modulated(QAM) alphabet having a plurality of elements 208, including fourboundary elements 310 (shown by “X”). For the square lattice 202, theboundary elements 310 are located at each corner. In alternativeembodiments, lattices could be another two-dimensional shape (e.g., arectangle, circle or ellipse) or a higher-dimensional shape (e.g., asphere, an ellipsoid, a hypersphere, a hyperellipsoid, or ahyperparallelopiped). In such cases, additional or fewer boundaryelements 310 may be used. In the case of circles, ellipses or othercurved lattice surfaces, boundary elements 310 may define a curve ratherthan a corner.

In FIG. 3, the boundary element 310 at the bottom left corner of thelattice 202 is at the origin. After passing through a lineartransformation (i.e., the matrix H) 204, the lattice 202 has beentransformed into the lattice 206. As shown, the corner elements 310 ofthe lattice 202 remain the corner elements 310 of the transformedlattice 206. In at least some embodiments, this result is due todefining the integer alphabet such that one of the corner elements 308is at the origin. Because the corner elements 310 are known, boundarylines 312 can be determined. Subsequently, elements 208 in thetransformed space can be compared to the boundary lines 312 to determinewhether or not elements 208 are within the boundary lines 312. As shown,some elements may be outside the boundary lines 312 and can thus beeliminated as candidates. The same boundary concept extends to higherdimensions and prevents searches outside of the lattice. For simplicity,the lattice 202 may be constrained to the 1^(st) quadrant and may becomposed only of integer elements. However, alternative embodiments mayvary with respect to quadrant location and/or with respect tocomposition (i.e., integer or non-integer elements).

FIG. 4 illustrates a MMSE LR-aided Multiple-Input Multiple-Output (MIMO)detector 400 in accordance with embodiments of the disclosure. AnLR-aided detector such as detector 400 operates in three steps. First,the detector 400 performs lattice reduction to find a reduced basis{tilde over (H)}=HT in block 402. As used herein, T refers to aunimodular matrix having integer entries, where the absolute value ofT's determinant is 1. Second, the detector 400 adapts the viewpointr′={tilde over (H)}c+ω′ by adding the output of block 402 with ω′ (usingadder 404) and implements a low-complexity MIMO detector (e.g., a linearor decision-feedback detector) to recover c. As used herein, c refers toa shifted and scaled version of the channel input. In FIG. 4, blocks406, 408 and 410 represent a technique for estimating c asĉ_(LR-MMSE)=[{tilde over (H)} ⁺ r′], where

${\underset{\_}{\overset{\sim}{H}} = {\begin{bmatrix}H \\{\sigma\; I}\end{bmatrix}T}},{{\underset{\_}{r}}^{\prime} = {\left\lbrack {r^{T},0} \right\rbrack^{T}\mspace{14mu}{{and}\mspace{14mu}\lbrack \cdot \rbrack}}}$denotes a component-wise rounding to integers. In at least someembodiments, estimating ĉ involves performing the lattice boundingoperation and eliminating candidates outside the boundary as describedherein. Third, the detector 400 recovers the inputs to the originalchannel using the relationship b=Tc in block 412. In FIG. 4, b isestimated as {circumflex over (b)}=[Tĉ]_(B), where [•]_(B) denotes acomponent-wise rounding to the nearest element of B.

When performing LR-aided detection, a common approach is to pass a1^(st) quadrant alphabet through a linear transformation and additivenoise, where detection in the translated space is performed by roundingto the nearest integer as described for FIG. 4. Unfortunately, detectionat this stage cannot guarantee that the estimated symbol trulycorresponds to a point in the original lattice. To verify that theestimated symbol corresponds to a point in the original lattice, theestimate is passed back through the inverse transformation which is yetanother matrix multiplication. Then the estimate is compared to thetransmitted alphabet adding further complexity.

With the lattice bounding operation, the number of matrixmultiplications can be reduced from two to one. Further, the need fortaking the matrix inverse is eliminated for translated elements that areoutside the boundary. In other words, establishing boundaries in thereceived space (after linear transformation) enables a comparison ofreceived points against the lines of the bounded lattice. One way toperform the boundary check is to determine whether a candidate is on theinterior of each boundary line (e.g., the lines 312). If a candidate isoutside the established boundaries, the candidate is presumed to beinvalid and the inverse transformation and comparison (to the originallattice) steps described previously can be omitted. Alternatively, if acandidate is within the established boundaries, the inversetransformation and comparison steps can be performed to guarantee thecandidate truly corresponds to a point in the original lattice.

FIG. 5 shows a block diagram of a receiver 500 in accordance withembodiments of the disclosure. In FIG. 5, the channel output block 502represents an incoming signal from a channel (e.g., a MIMO channel). Insome embodiments, the channel output (r) is provided to a channelestimation block 504, which estimates the MIMO channel and outputs thechannel matrix H. In other embodiments, the channel matrix H may havebeen estimated previously by other means and stored. The channel outputr is also provided to a noise-variance estimation block 514, whichestimates the noise variance ({circumflex over (σ)}²) of the channeloutput r. As shown, an equalization block 406 equalizes the channeloutput r and the channel matrix H yielding the equalized channel outputy and the equalized channel matrix R.

The receiver 500 also has a lattice boundary computation block 510,which receives the channel matrix H and outputs boundary information tothe detector 512. For example, the boundary information may correspondto the translated version of corner points or boundary points from theoriginal set of all possible input symbol vectors to the receiver 500.The detector 512 then detects incoming signals based on the equalizedchannel output y, the equalized channel matrix R and the boundaryinformation. The output of the detector 512 is forwarded to a decoder514, which decodes the incoming signal. The bounding operation canadvantageously reduce the computational burden of the receiver 500 byreducing the number of matrix multiplications (inverse transformations)and subsequent comparisons performed for detection. The blocks of FIG. 5can be representative of hardware, firmware, and/or software as would beunderstood by one of skill in the art.

FIG. 6 shows an illustrative embodiment of a wireless communicationsystem 600 in accordance with embodiments of the invention. As shown,the wireless communication system 600 comprises a MIMO transmitter 602having at least one antenna 606 for transmitting radio frequency signalsreceived as input 612. The MIMO transmitter 602 may represent a fixed orportable wireless device, a cellular phone, a personal digitalassistant, a wireless modem card, or any other device configured totransmit on a MIMO wireless network. In FIG. 1, a MIMO receiver 604 isconfigured to receive radio frequency signals transmitted by the MIMOtransmitter 602. The MIMO receiver 604 has at least one antenna 608 forreceiving transmitted radio frequency signals.

As shown, the MIMO transmitter 602 transmits radio frequency signals tothe MIMO receiver 604 through a channel 610. While MIMO systems maygreatly increase spectral efficiency, the process of separating signalssimultaneously transmitted from multiple antennas 606 may be burdensomefor the MIMO receiver 604. To reduce the computational burden, the MIMOreceiver 604 comprises a lattice boundary tester 616, which efficientlyeliminates candidates determined to be outside the establishedboundaries of a translated lattice search space. In at least someembodiments, the lattice boundary tester 616 comprises anApplication-Specific Integrated Circuit (ASIC) that receives the channelmatrix as input and then outputs boundary information to thedetector/decoder 614. The boundary information could take a number offorms. In at least some embodiments, the boundary informationcorresponds to the translated version of corner points or boundarypoints from the original set of all possible input symbol vectors to thereceiver 604.

FIG. 7 illustrates an electronic device 702 in accordance withembodiments of the disclosure. Electronic devices such as the device 702communicate wirelessly (or via a wired connection) using a variety oftechniques to prepare, send, receive, and recover data. For example,data preparation techniques may include data scrambling, errorcorrection coding, interleaving, data packet formatting, and/or othertechniques. The data to be transmitted is converted into blocks of data(i.e., bits) transmitted as information symbols. Each information symbolis associated with a constellation of complex amplitudes.

If data communication is wireless, the electronic device 702 may employone or more antennas to “pick up” wireless signals, after which data isrecovered by sampling the received signal and decoding each informationsymbol. To recover data, the electronic device 702 may implementtechniques such as signal amplification, digitization, sample rateconversion, data correlation, equalization, demodulation,de-interleaving, de-coding, and/or de-scrambling.

The electronic device 702 may represent any of a variety of devices suchas a server, a desktop computer, a laptop computer, a cellular phone, aPersonal Digital Assistant (PDA), a smart phone or other electronicdevices. In various embodiments, the electronic device 702 receivescommunications based on an 802.11(a), (g), or (n) protocol, a WorldwideInteroperability of Microwave Access (WiMAX) protocol, an Ultra Wideband(UWB) protocol, a Long-Term Evolution (LTE) protocol or some othercommunication protocol now known or later developed.

As shown, the electronic device 702 comprises a processor 704 coupled toa memory 706 and a transceiver 710. The memory 706 stores applications708 for execution by the processor 704. The applications 708 couldcomprise any known or future application useful for individuals ororganizations. As an example, such applications 608 could be categorizedas operating systems, device drivers, databases, presentation tools,emailers, file browsers, firewalls, instant messaging, finance tools,games, word processors or other categories. Regardless of the exactnature of the applications 708, at least some of the applications 708may rely on signals received via the transceiver 710.

To more efficiently process received signals, the transceiver 710employs a lattice detector 720 having a lattice boundary tester 722. Thelattice boundary tester 722 includes a boundary definer 724 and acandidate-to-boundary comparator 726. In at least some embodiments, theboundary definer 724 identifies corner points or boundary points of atranslated lattice based on the original (untranslated) set of allpossible input symbol vectors to the transceiver 710. Once the boundaryis defined, the candidate-to-boundary comparator 726 can compare points(candidates) in the translated space to the boundaries. If a candidateis outside the established boundaries, the candidate is presumed to beinvalid and further processing for the candidate (e.g., inversetransformation and comparison to points of the original lattice) can beomitted. If a candidate is within the established boundaries, thelattice detector 720 may perform the inverse transformation andcomparison steps to guarantee the candidate truly corresponds to a pointin the original lattice.

FIG. 8 illustrates a wireless signal detection method 800 in accordancewith embodiments of the disclosure. The method 800 comprises identifyinga boundary for a translated lattice (block 802). The method 800 alsocomprises eliminating candidates that are outside the boundary (block804). In at least some embodiments, identifying the boundary involvesdetermining corner points or boundary points of a transformed lattice.If a candidate is outside the established boundaries, the candidate ispresumed to be invalid and further processing for the candidate (e.g.,inverse transformation and comparison to points of the original lattice)can be omitted. Thus, the method 800 can reduce the computational burdenof wireless signal detection.

While several embodiments have been provided in the present disclosure,it should be understood that the disclosed systems and methods may beembodied in many other specific forms without departing from the spiritor scope of the present disclosure. The present examples are to beconsidered as illustrative and not restrictive, and the intention is notto be limited to the details given herein, but may be modified withinthe scope of the appended claims along with their full scope ofequivalents. For example, the various elements or components may becombined or integrated in another system or certain features may beomitted, or not implemented.

Also, techniques, systems, subsystems and methods described andillustrated in the various embodiments as discrete or separate may becombined or integrated with other systems, modules, techniques, ormethods without departing from the scope of the present disclosure.Other items shown or discussed as directly coupled or communicating witheach other may be coupled through some interface or device, such thatthe items may no longer be considered directly coupled to each other butmay still be indirectly coupled and in communication, whetherelectrically, mechanically, or otherwise with one another. Otherexamples of changes, substitutions, and alterations are ascertainable byone skilled in the art and could be made without departing from thespirit and scope disclosed herein.

1. A wireless communication system, comprising: a transmitter thattransmits a Multiple-input Multiple-Output (MIMO) signal over acommunication channel; a receiver that receives the MIMO signal as anoutput of the communication channel, a lattice detector comprising: aboundary definer which establishes a hypercube boundary for atransformed integer lattice, wherein said integer lattice definesdiscrete subgroup of a space spanning a real vector space generated froma basis with integer coefficients; and a candidate-to-boundarycomparator which checks whether received candidate points are within atransformed integer lattice hypercube boundary, wherein the systemeliminates candidates outside the established boundary.
 2. The wirelesscommunication system of claim 1 wherein the hypercube boundary isdefined by at least one corner.
 3. The wireless communication system ofclaim 1 wherein the receiver performs an inverse transformation only forcandidates determined to be within the established hypercube boundary.4. The wireless communication system of claim 3 wherein, after eachinverse transformation, the receivercandidate-to-boundary comparatorcompares candidates to points in an original integer lattice.
 5. Thewireless communication system of claim 1, wherein the receiverimplements at least one detector that relies on the hypercube boundary,the at least one detector selected from the group consisting of aMinimum Mean-Squared Error (MMSE) Lattice-Reduction Aided (LR)Multiple-input Multiple-Output (MIMO) detector, a Soft InterferenceCancellation (SIC) LR MIMO detector, and a zero-forcing (ZF) LR MIMOdetector.
 6. An electronic device, comprising: a processor; and areceiver coupled to the processor, the receiver comprising a latticedetector comprising: a boundary definer for identifying boundary points;a candidate-to-boundary comparator which checks whether receivedcandidate points are within a transformed integer lattice hypercubeboundary, wherein said integer lattice defines discrete subgroup of aspace spanning a real vector space generated from a basis with integercoefficients.
 7. The electronic device of claim 6 wherein the receivereliminates candidate points determined to be outside the transformedinteger lattice hypercube boundary.
 8. The electronic device of claim 6wherein the boundary definer identifies at least one corner to establishthe transformed integer lattice hypercube boundary.
 9. The electronicdevice of claim 6 wherein the receiver performs an inversetransformation only for candidates determined to be within thetransformed integer lattice hypercube boundary.
 10. The electronicdevice of claim 9 wherein, after each inverse transformation, thecandidate-to-boundary comparator compares candidates to points in anoriginal integer lattice.
 11. A method for wireless signal detection,comprising: identifying a plurality of corners of a hypercube boundaryfor a transformed integer lattice, wherein said integer lattice definesdiscrete subgroup of a space spanning a real vector space generated froma basis with integer coefficients; and eliminating candidates that areoutside the hypercube boundary.
 12. The method of claim 11 furthercomprising performing an inverse transformation only for candidatesdetermined to be within the hypercube boundary.
 13. The method of claim12 further comprising, after each inverse transformation, comparescandidates to points in an original integer lattice.
 14. The method ofclaim 11 further comprising reducing an integer lattice beforeidentifying the hypercube boundary.